Basic instruments of differential and integral calculus for functions of one real variable. Basic functions. Limits and continuity. Derivative, its geometrical interpretation, its meaning in the applied sciences. Basic theorems and methods of differential calculus. Definite integral, its meaning in terms of area and in the applied sciences. Fundamental theorem of calculus.
J. Stewart, Calcolo, funzioni di una variabile. (an english version is available)
Learning Objectives
Knolewdge acquired: elementary functions (linear, polynomials, exponential, logarithm) and examples of their use in the applied sciences;
concept of derivative and definite integral (geometric meaning, significance in the applied sciences) and of their main applications.
Competence acquired (at the end of the course):
ability to understand which problems can be solved via the use of derivatives and integrals.
Skills acquired (at the end of the course): manipulation of elementary functions, computation of derivatives and their use to study monotonicity and maxima of a function; drawing the graph of a function with or without the help of a suitable software, computation of a numerical approximation of a definite integral
Prerequisites
Courses required: none
Courses recommmended: none
Teaching Methods
CFU: 9
Lezioni di didattica frontale (totale ore): 50 Contact hours for:
Lectures:50
Attività di laboratorio (totale ore):30 Laboratory/practice: 30
Seminari/visite guidate (totale ore): 0 Seminars/excursions: 0
Further information
Frequency of lectures, practice and lab: although non compulsory, is strongly recommended
Teaching tools:
Video projector, PC
Type of Assessment
Written and oral exam
Course program
Basic instruments of differential and integral calculus for functions of one real variable. Basic functions. Limits and continuity. Derivative, its geometrical interpretation, its meaning in the applied sciences. Basic theorems and methods of differential calculus. Definite integral, its meaning in terms of area and in the applied sciences. Fundamental theorem of calculus.